求积分(1-x)的平方/根号x.
问题描述:
求积分(1-x)的平方/根号x.
答
(1-x)的平方/根号x=1/√x -2√x+x^(3/2)=x^(-1/2)-2x^(1/2)+x^(3/2)
=>∫[(1-x)的平方/根号x]dx =∫[x^(-1/2)-2x^(1/2)+x^(3/2)]=...
幂函数的积分,你会的。我没答题器,不好打,你自己做完,好吗?
答
∫ (1 - x)²/√x dx= ∫(1 - 2x + x²)/√x dx= ∫ x^(- 1/2) dx - 2∫ x^(1/2) dx + ∫ x^(3/2) dx= x^(1 - 1/2)/(1 - 1/2) - 2x^(1 + 1/2)/(1 + 1/2) + x^(1 + 3/2)/(1 + 3/2) + C= 2√x - 2 * 2/3 * x^(...